A commuting-based refinement of the contiguity matrix for spatial models, and an application to local police expenditures

One of the main weaknesses of empirical models in regional science and urban economics involving spatial interdependence is the arbitrary nature of the weight matrix. The paper considers a refinement of the commonly used contiguity matrix which exploits information on commuting flows between locations. Within the set of contiguous jurisdictions, the matrix assigns higher weights to localities for which commuting patterns suggest that households would view them as substitute locations to reside in. The concept is then applied to cities and townships in New England. Using the expenditure competition effect on local police spending as an example, we show that commuting-adjusted weighting schemes give estimates which differ substantially from those obtained using a standard contiguity matrix.